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Academic literature on the topic 'Random Walk Tours'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Random Walk Tours"

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BRÉMONT, JULIEN. "RANDOM WALK IN QUASI-PERIODIC RANDOM ENVIRONMENT." Stochastics and Dynamics 09, no. 01 (March 2009): 47–70. http://dx.doi.org/10.1142/s0219493709002543.

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We consider a one-dimensional random walk with finite range in a random medium described by an ergodic translation on a torus. For regular data and under a Diophantine condition on the translation, we prove a central limit theorem with deterministic centering.
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Windisch, David. "Random walk on a discrete torus and random interlacements." Electronic Communications in Probability 13 (2008): 140–50. http://dx.doi.org/10.1214/ecp.v13-1359.

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Hoyer, Peter, and Zhan Yu. "Analysis of lackadaisical quantum walks." Quantum Information and Computation 20, no. 13&14 (November 2020): 1138–53. http://dx.doi.org/10.26421/qic20.13-14-4.

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The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other classes of vertex-transitive graphs. Our proof establishes and uses a relationship between lackadaisical quantum walks and quantum interpolated walks for any regular locally arc-transitive graph.
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Markovski, Smile, Danilo Gligoroski, and Jasen Markovski. "Classification of quasigroups by random walk on torus." Journal of Applied Mathematics and Computing 19, no. 1-2 (March 2005): 57–75. http://dx.doi.org/10.1007/bf02935788.

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Teixeira, Augusto, and David Windisch. "On the fragmentation of a torus by random walk." Communications on Pure and Applied Mathematics 64, no. 12 (July 20, 2011): 1599–646. http://dx.doi.org/10.1002/cpa.20382.

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Procaccia, Eviatar B., and Eric Shellef. "On the range of a random walk in a torus and random interlacements." Annals of Probability 42, no. 4 (July 2014): 1590–634. http://dx.doi.org/10.1214/14-aop924.

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JUNGREIS, DOUGLAS. "GAUSSIAN RANDOM POLYGONS ARE GLOBALLY KNOTTED." Journal of Knot Theory and Its Ramifications 03, no. 04 (December 1994): 455–64. http://dx.doi.org/10.1142/s0218216594000332.

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A Gaussian random walk is a random walk in which each step is a vector whose coordinates are Gaussian random variables. In 3-space, if a Gaussian random walk of n steps begins and ends at the origin, then we can join successive points by straight line segments to get a knot. It is known that if n is large, then the knot is non-trivial with high probability. We give a new proof of this fact. Our proof shows in addition that with high probability the knot is contained as an essential loop in a fat, knotted, solid torus. Therefore the knot is a satellite knot and cannot be unknotted by any small perturbation.
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Prescott, Timothy, and Francis Edward Su. "Random walks on the torus with several generators." Random Structures and Algorithms 25, no. 3 (2004): 336–45. http://dx.doi.org/10.1002/rsa.20029.

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Černý, Jiří, and Augusto Teixeira. "Random walks on torus and random interlacements: Macroscopic coupling and phase transition." Annals of Applied Probability 26, no. 5 (October 2016): 2883–914. http://dx.doi.org/10.1214/15-aap1165.

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Deng, Youjin, Timothy M. Garoni, Jens Grimm, and Zongzheng Zhou. "Unwrapped two-point functions on high-dimensional tori." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 5 (May 1, 2022): 053208. http://dx.doi.org/10.1088/1742-5468/ac6a5c.

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Abstract We study unwrapped two-point functions for the Ising model, the self-avoiding walk (SAW) and a random-length loop-erased random walk on high-dimensional lattices with periodic boundary conditions. While the standard two-point functions of these models have been observed to display an anomalous plateau behaviour, the unwrapped two-point functions are shown to display standard mean-field behaviour. Moreover, we argue that the asymptotic behaviour of these unwrapped two-point functions on the torus can be understood in terms of the standard two-point function of a random-length random walk model on Z d . A precise description is derived for the asymptotic behaviour of the latter. Finally, we consider a natural notion of the Ising walk length, and show numerically that the Ising and SAW walk lengths on high-dimensional tori show the same universal behaviour known for the SAW walk length on the complete graph.
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Book chapters on the topic "Random Walk Tours"

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Drewitz, Alexander, Balázs Ráth, and Artëm Sapozhnikov. "Random Walk on the Torus and Random Interlacements." In SpringerBriefs in Mathematics, 19–29. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05852-8_3.

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Yor, Marc. "Etude asymptotique des nombres de tours de plusieurs mouvements browniens complexes corrélés." In Random Walks, Brownian Motion, and Interacting Particle Systems, 441–55. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0459-6_25.

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Conference papers on the topic "Random Walk Tours"

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Biswas, Aritro, and Bhaskar Krishnamachari. "Modeling the Expected Data Collection Time for Vehicular Networks Using Random Walks on a Torus." In 2014 IEEE 11th International Conference on Mobile Ad Hoc and Sensor Systems (MASS). IEEE, 2014. http://dx.doi.org/10.1109/mass.2014.62.

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